Question

How do you find value of discriminant then describe number and type of solutions for `x^2 - 16x + 64 = 0`?

Answer 1

Discriminant value is 0. The solution is that both the roots would be equal to 8

Explanation:

Solution of a general quadratic equation of the form `ax^2+bx+c=0` is `x=(-b+-sqrt (b^2-4ac))/(2a)` .

The expression inside the radical sign is called the Discriminant. There are two solutions (called roots) one each with a + and - sign in front of the radical. There are three possibilities of the Discriminant being <0, >0 or =0. Accordingly, if the Discriminant is <0, the roots are not real, they are imaginary. Secondly, if the Discriminant is >0, the roots are real and distinct. Lastly if the Discriminant =0, both the roots are equal.

In the present case, comparing the coefficients with the general equation, a=1, b= -16 and c=64. Thus the Discriminant would be `(-16)^2 -4(1)(64)` = 0. Hence the solution would be both the roots being equal to 8